to the plane of the orbit PAB) beſides the perturbation of the motion juſt now ſpoken of as to longitude. introduces another perturbation alſo as to latitude, attracting the body P out of the plane of its orbit. And this perturbation, in any given ſituation of the bodies P and T to each other, will be as the generating force MN; and therefore becomes leaſt when the force MN is leaſt, that is, (as was juſt now ſhewn) where the attraction 5N is not much greater nor much leſs than the attraction SK. Q. E. D.
Cor. 1.. Hence it may be eaſily collected, that if ſeveral leſs bodies P, S, R, &c. revolve about a very great body T; the motion of the innermoſt revolving body P will be leaſt diſturbed by the attractions of the others. when the great body is as well attracted and agitated by the reſt (according to the ratio of the accelerative forces) as the reſt are by each other mutually.
Cor. 2. In a ſyſtem of three bodies T, P, S, if the accelerative attractions of any two of them towards a third be to each other reciprocally as the ſquares of the diſtances; the body P, by the radius PT; will deſcribe its area ſwifter near the conjunction A and the opposition B, than it will near the quadratures C and D. For every force with which the body P is acted on and the body T is not, and which does not act in the direction of the line PT; does either accelerate or retard the deſcription of the area, according as it is directed, whether in conſequentia or in antecedentia. Such is the force NM. This force in the paſſage of the body P from C to A is directed in conſequentia to its motion, and therefore accelerates it; then as far as D in antecedentia, and retards
